To overcome these challenges, one can project the original detection problem in a high-dimensional space to a low-dimensional space by exploiting its specific structure [1]}. In addition, if the apriori knowledge of the device state matrix that needs to be recovered is available in advance, the required length of the pilot sequences can be shortened for a given performance requirement. For example, the AMP algorithms improved the detection performance by modeling the device state matrix as a Bernoulli-Gaussian distributed random matrix based on the assumptions that uplink channels were Gaussian distributed [2]}. These assumptions, however, still have limitations, since wireless channels in practical environments often exhibit much more complex statistical structures. Specifically, some research works in [3]}-[4]} have shown that the channels in massive multiple-input multiple-output (MIMO) systems exhibit spatial sparsity, which can be approximated by the Gaussian mixture distribution. As a result, the interested device state matrix is a Bernoulli-Gaussian mixture distributed random matrix. Based on such a distribution, the detection performance can be improved in practical scenarios. However, it is not trivial to obtain the parameters of the Bernoulli-Gaussian mixture distribution by employing traditional channel estimation approaches.
